MMBCV: Bias-corrected cluster-robust sandwich variance for multistate Cox models

Description

Computes several sandwich variance estimators (robust, MR, MD, FG, KC, MBN and combinations) for multistate Cox models using cluster-level score aggregation, with Breslow or Efron ties.

Usage

MMBCV(
  fit,
  data,
  StartTime,
  StopTime,
  ClusterID,
  SubjectID,
  Event,
  tie = c("breslow", "efron"),
  details = FALSE,
  detail_names = NULL,
  kc_tol = 1e-10
)

Arguments

Value

A list containing variance-covariance matrices:

robust

Standard cluster-robust sandwich variance estimator.

varMR

Martingale-residual (MR) bias-corrected variance estimator.

varMD

Mancl-DeRouen (MD) bias-corrected variance estimator.

varMDMR

Hybrid Mancl-DeRouen plus martingale-residual (MDMR) bias-corrected variance estimator.

varFG

Fay-Graubard (FG) bias-corrected variance estimator.

varFGMR

Hybrid Fay-Graubard plus martingale-residual (FGMR) bias-corrected variance estimator.

varKC

Kauermann-Carroll (KC) bias-corrected variance estimator.

varKCMR

Hybrid Kauermann-Carroll plus martingale-residual (KCMR) bias-corrected variance estimator.

varMBN

Morel-Bokossa-Neerchal (MBN) bias-corrected variance estimator.

varMBNMR

Hybrid Morel-Bokossa-Neerchal plus martingale-residual (MBNMR) bias-corrected variance estimator.

If details = TRUE, additional intermediate matrices may also be returned.

References

Wang, X., Turner, E. L., and Li, F. (2023). Improving sandwich variance estimation for marginal Cox analysis of cluster randomized trials. Biometrical Journal, 65, 2200113.

Schaubel, D. E. (2005). Adjusting analytic inference for small samples in recurrent event regression. Statistics in Medicine, 24(19), 3037–3051.

Kauermann, G., and Carroll, R. J. (2001). A note on the efficiency of sandwich covariance matrix estimation. Journal of the American Statistical Association, 96(456), 1387–1396.

Fay, M. P., and Graubard, B. I. (2001). Small-sample adjustments for Wald-type tests using sandwich estimators. Biometrics, 57(4), 1198–1206.

Mancl, L. A., and DeRouen, T. A. (2001). A covariance estimator for GEE with improved small-sample properties. Biometrics, 57(1), 126–134.

Morel, J. G., Bokossa, M., and Neerchal, N. K. (2003). Small sample correction for the variance of GEE estimators. Biometrical Journal, 45(4), 395–409.

Therneau, T., Crowson, C., and Atkinson, E. (2026). Multi-state models and competing risks. Vignette for the survival package. See vignette("compete", package = "survival") or https://CRAN.R-project.org/package=survival.

See Also

coxph, Surv

Examples

data("msdat3")

# Example requires the suggested package 'survival'
if (requireNamespace("survival", quietly = TRUE)) {
  fit <- survival::coxph(
    list(
      survival::Surv(Tstart, Tstop, event) ~ 1,
      state("(s0)"):state("S1") + state("S1"):state("S2") + state("S2"):state("S3") ~
        Z + X,
      state("(s0)"):state("D") + state("S1"):state("D") + state("S2"):state("D") +
        state("S3"):state("D") ~ (Z + X)/common
    ),
    data = msdat3, id = id, ties = "breslow",
    timefix = FALSE
  )

  MMBCV(
       fit       = fit,
       data      = msdat3,
       StartTime = Tstart,
       StopTime  = Tstop,
       ClusterID = clus_id,
       SubjectID = id,
       Event     = event,
       tie       = "breslow",
       details   = FALSE)
}

Clustered multistate simulated dataset (counting-process format)

Description

A simulated clustered, subject-level multistate dataset in long (counting-process) format. Treatment is assigned at the cluster level and baseline covariates are available at both the cluster and individual levels. Each subject may contribute multiple rows, corresponding to transitions between states over time.

Usage

data(msdat3)

Format

A data frame with 3,004 rows and 9 variables:

id

Subject identifier. There are 1,500 unique subjects.

Z

Cluster-level treatment assignment indicator. Z = 1 indicates the cluster is assigned to treatment; Z = 0 indicates control.

X

Individual-level baseline covariate generated from a standard normal distribution.

clus_id

Cluster identifier. There are 30 clusters.

from

Starting state for the current observation interval (e.g., (s0)).

to

Ending state for the current observation interval (e.g., S1, S2, S3, D, or censor).

Tstart

Start time of the interval.

Tstop

Stop time of the interval.

event

End state at Tstop. Values include censor, S1, S2, S3, and D, where D is the absorbing state.

Details

The multistate process uses the following state labels:

• (s0): initial (starting) state.

• S1: first intermediate transition state.

• S2: second intermediate transition state.

• S3: third intermediate transition state.

• D: absorbing (terminal) state.

Each row represents a time interval [Tstart, Tstop] during which the subject is at risk for the transition indicated by from and to. The variable event records the state at which the interval ends. event = "censor" indicates the observation is right-censored at Tstop (i.e., no transition is observed at the end of the interval).

The distribution of event in this dataset is:

• censor: 1050

• S1: 837

• S2: 450

• S3: 217

• D: 450

Source

Simulated data bundled with the package for examples and testing.

Examples

data("msdat3")
nrow(msdat3)
length(unique(msdat3$id))
length(unique(msdat3$clus_id))
table(msdat3$event)

Subset a dataset by transition using a row map

Description

Subset a dataset by transition using a row map

Usage

subset_by_transition(dataA, dataB, transition)

Arguments

Value

A named list of data frames, one per transition.